On the impact deformation of an incompressible half-space under the action of a shear load of variable direction

A loading process in which the shear action on the boundary plane changes both in intensity and direction is considered on the example of a one-dimensional plane problem for a nonlinear elastic incompressible half-space. We show that, in the domains of the space where the nonlinearity of the system becomes a substantial factor, in the front region of the shock wave, the solution is determined by a system of nonlinear evolution equations. We obtain the general solution to the evolution system. As an example, we consider a particular solution to the evolution system for one of the simplest boundary conditions. We also expose a parametric method for finding the displacements on the basis of a solution to the evolution system.